It has not been generally known, hitherto, that Oughtred designed a
rectilinear slide rule for gauging and published a description thereof in
1633.[26] In his Circles of Proportion, chapter IX, Oughtred had offered a
closer approximation than that of Gunter for the capacity of casks. The
Gauger of London expostulated with Oughtred for presuming to question
anything that Gunter had written. The ensuing discussion led to an
invitation extended by the Company of Vintners to the instrument maker
Elias Allen to request Oughtred to design a gauging rod.[27] This he did,
and Allen received an order for “threescore” instruments. On page 19
Oughtred describes his ‘Gauging Rod:’
It consisteth of two rulers of brasse about 32 ynches of length, which
also are halfe an ynch broad, and a quarter of an ynch thick . . . At one
end of both those rulers are two little sockets of brasse fastened on
strongly: by which the rulers are held together, and made to move one
upon another, and to bee drawne out unto any length, as occasion shall
require: and when you have them at the just length, there is upon one of
the sockets a long Scrue-pin to scrue them fast.
There are graduations on three sides of the rulers, one graduation being
the logarithmic line of numbers. He says (p. 39), “the maner of computing
the Gauge-divisions I have concealed.” W. Robinson, who was a friend of
Oughtred, wrote him as follows:[28]
I have light upon your little book of artificial gauging, wherewith I am
much taken, but I want the rod, neither could I get a sight of one of
them at the time, because Mr. Allen had none left . . . I forgot to ask
Mr. Allen the price of one of them, which if not much I would have one of
them.” Oughtred annotated this passage thus: “Or in wood, if any be made
in wood by Thompson or any other.”
Another of Oughtred’s admirers, Sir Charles Cavendish, wrote, on February
11, 1635 thus:[29]
I thank you for your little book, but especially for the way of
calculating the divisions of your gauging rod. I wish, both for their own
sakes and yours, that the citizens were as capable of the acuteness of
this invention, as they are commonly greedy of gain, and then I doubt not
but they would give you a better recompense than I doubt now they will.
On April 20, 1638, we find Oughtred giving Elias Allen directions[30]
“about the making of the two rulers.” As in 1633,[31] so now, Oughtred
takes one ruler longer than the other. This 1633 instrument was used also
as “a crosse-staffe to take the height of the Sunne, or any Starre above
the Horizon, and also their distances.” The longer ruler was called staffe,
the shorter transversarie. While in 1633 he took the lengths of the two in
the ratio “almost 3 to 2,” in 1638, he took “the transversary three
quarters of the staff’s length, . . . that the divisions may be larger.”